Question: Solve for $x$ and $y$ using elimination. ${-2x+4y = 32}$ ${2x+3y = 38}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $7y = 70$ $\dfrac{7y}{{7}} = \dfrac{70}{{7}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x+4y = 32}\thinspace$ to find $x$ ${-2x + 4}{(10)}{= 32}$ $-2x+40 = 32$ $-2x+40{-40} = 32{-40}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 10}$ into $\thinspace {2x+3y = 38}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(10)}{= 38}$ ${x = 4}$